1. Field of Invention
Aspects of the invention relate to a method for and software program for the surveying and engineering communities, for instance those involved in right-of-way engineering, and Geographic Information Systems (GIS) and Land Information Systems (LIS) specialists, and in particular, a method for and software program for two-dimensional coordinate transformations.
2. Background
There exist products which offer only the 4-parameter linear transformation, which is a useful transformation for most surveyors, but does not adequately address the needs of Geographic Information Systems (GIS) and Land Information Systems (LIS) specialists. GIS/LIS specialists need transformations that will adequately address the problem of transforming existing map data from one projection system to another, for instance data from an Albers equal-area projection to a conformal projection in the State Plane Coordinate System. A user should be aware before even attempting a transformation under these circumstances that the scale in the directions of the x and y-axis will be different, which would almost certainly dictate an affine or general bivariate polynomial transformation of the 2nd to 5th power. In some instances, an 8-parameter projective transformation would be better. Therefore, there exists a need for a very quick method of computing any of these transformations, along with map accuracy statistics, which will yield instantaneous information for a valid comparison.
Presently, there are no known programs that offer Conformal Polynomial Transformations. Conformal Polynomial Transformations are particularly useful when a surveyor or GIS/LIS professional wants to hold all of the transformed System 2 control coordinate pairs to the exact value of the corresponding System 1 control coordinate pairs, and at the same time ensure that the shape of any figure defined in the System 1 Cartesian plane will be best preserved.
For a transformation to be defined as conformal, the following Cauchy-Riemann equations must be satisfied:δX/δx=δY/δy and; δX/δy=−δY/δx 